Connection between the packing efficiency of binary hard spheres and the glass-forming ability of bulk metallic glasses

Abstract

We perform molecular dynamics simulations to compress binary hard spheres into jammed packings as a function of the compression rate R, size ratio α, and number fraction x(S) of small particles to determine the connection between the glass-forming ability (GFA) and packing efficiency in bulk metallic glasses (BMGs). We define the GFA by measuring the critical compression rate R(c), below which jammed hard-sphere packings begin to form "random crystal" structures with defects. We find that for systems with α≳0.8 that do not demix, R(c) decreases strongly with Δϕ(J), as R(c)∼exp(-1/Δϕ(J)(2)), where Δϕ(J) is the difference between the average packing fraction of the amorphous packings and random crystal structures at R(c). Systems with α≲0.8 partially demix, which promotes crystallization, but we still find a strong correlation between R(c) and Δϕ(J). We show that known metal-metal BMGs occur in the regions of the α and x(S) parameter space with the lowest values of R(c) for binary hard spheres. Our results emphasize that maximizing GFA in binary systems involves two competing effects: minimizing α to increase packing efficiency, while maximizing α to prevent demixing.

Beyond packing of hard spheres: The effects of core softness, non-additivity, intermediate-range repulsion, and many-body interactions on the glass-forming ability of bulk metallic glasses

“…We first equilibrated liquid states at packing fraction φ = 0.25. To compress the system, we ran the MD simulations at constant volume for a time interval τ , and then compressed the system instantaneously until the closest pair of spheres came into contact [15,23]. We performed successive compressions until the pressure increased to 10 3 , which corresponds to (φ J −φ)/φ J < 10 −3 , where φ J is the packing fraction at the onset of jamming.…”

“…In contrast, the main source of geometric frustration in alloys is the mismatch between atomic sizes [19][20][21][22][23][24]. Molecular dynamics simulations of binary hard spheres have shown that tuning the atomic size ratio can decrease R c by more than 13 orders of magnitude [15]. Packing of hard spheres can also rationalize the correlation between the number of components, their atomic size ratios, and the GFA of BMGs [8].…”

Computer simulations of glasses: the potential energy landscape

“…Moreover, hard spheres are surprisingly good at explaining the glassforming ability of bulk metallic glasses, which are characterised by weak, non-directional interactions. In a binary hard sphere system, the best glass formers have an atomic size ratio that compromises between two competing pressures: minimising it to improve the packing efficiency, and maximising it to prevent phase separation [233].…”

Long-lived non-equilibrium interstitial solid solutions in binary mixtures

“…Very recent developments in electron microscopy have for the first time allowed us to analyse the disorder of an SSS of iron in platinum 3 . Also, High Entropy Alloys (HEAs), which are effectively a multicomponent SSS, are currently very actively studied as they are among the toughest materials known [4][5][6][7][8] . Hard spheres, as epitomised by colloids, are widely used as models to study the selfassembly and phase behaviour processes of atoms and molecules.…”

“…This large diversity of equilibrium structures highlights their potential for applications in photonics, optics, semiconductors and structure design 5,14,15,19 . In addition, due to their simplicity, binary hard sphere mixtures are ideal models to study the kinetics of crystallisation in salts, metal alloys, metallic glasses and any other crystallising system where there is more than one species, and so there is a compositional variable [4][5][6][7][8] .…”